Geodesic
Boundary control of fronts in a~Burgers-type equation with modular adhesion and periodic amplification
Teoretičeskaâ i matematičeskaâ fizika, Tome 212 (2022) no. 2, pp. 179-189

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We consider a singularly perturbed periodic problem for a Burgers-type equation with modular advection and periodic linear amplification. We obtain conditions for the existence, uniqueness, and asymptotic stability in the sense of Lyapunov of a periodic solution with an interior transition layer and construct its asymptotic approximation. The asymptotics of the solution is used to determine boundary conditions ensuring the implementation of a prescribed mode of the front motion, i.e., the boundary control problem. We also formulate the notion of an asymptotic solution of the boundary control problem and obtain sufficient conditions for the existence of the required periodic mode of the front motion.
Keywords: singularly perturbed parabolic equations, periodic problem, contrast structure, interior layer, moving front, asymptotic methods, differential inequalities, asymptotic stability in the sense of Lyapunov, Burgers equations with modular advection, boundary control problem, asymptotic solution of boundary control problem.
Mots-clés : reaction–diffusion–advection equations 
@article{TMF_2022_212_2_a1,
     author = {V.T. Volkov and N. N. Nefedov},
     title = {Boundary control of fronts in {a~Burgers-type} equation with modular adhesion and periodic amplification},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {179--189},
     publisher = {mathdoc},
     volume = {212},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2022_212_2_a1/}
}
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V.T. Volkov; N. N. Nefedov. Boundary control of fronts in a~Burgers-type equation with modular adhesion and periodic amplification. Teoretičeskaâ i matematičeskaâ fizika, Tome 212 (2022) no. 2, pp. 179-189. http://geodesic.mathdoc.fr/item/TMF_2022_212_2_a1/